Elementary function arithmetic

In proof theory, Harvey Friedman' grand conjecture implies that many mathematical theorems, such as Fermat's last theorem, can be proved in very weak systems.

References

Avigad, Jeremy (2003), "Number theory and elementary arithmetic", Philosophia Mathematica. Philosophy of Mathematics, its Learning, and its Application. Series III, 11 (3): 257–284, doi:10.1093/philmat/11.3.257, ISSN 0031-8019, MR2006194